Supporting Information Analysis Method for Quantifying the Morphology of Nanotube Networks Dusan Vobornik*, Shan Zou and Gregory P. Lopinski Measurement Science and Standards, National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario, K1A 0R6, Canada Corresponding Author *E-mail: dusan.vobornik@nrc.ca S1
Contents 1. Cross-sections: bundling of polymer dispersed nanotubes 2. AFM tip size estimation and de-convolution procedure 3. Deconvolved images 4. Uncertainty analysis based on height threshold to separate nanotubes from the substrate 5. References 1. Cross-sections: bundling of polymer dispersed nanotubes In figure S1 we show cross sections of several bundles in same nanotube images that are presented in the figure 1 of the article. These nanotubes have a narrow distribution of diameters ranging from 1.2 to 1.4 nm. Upon polymer wrapping, a further diameter increase can be expected, as AFM is then measuring the added polymer and nanotube diameters. Yet, at this time it is impossible to predict the exact diameter increase because it depends on the way in which the polymer wraps nanotubes and which is not known: the geometry of the wrapping (helical vs aligned with the nanotube axis), the wrapping density (are polymer molecules entirely covering the nanotube surface, or are there only sparse polymer molecules here and there along the nanotube), or the position adopted by polymers alkyl chains, all affect the eventual diameter increase. The polymer could not be directly resolved by AFM on the surface of nanotubes in our experiments. Based on cross-sections of 20 single nanotubes in all four images presented in figure 1 in the article, the average wrapped single nanotube size is 1.7 nm. Here the assumption is that any nanotube whose diameter does not exceed 2 nm in the AFM image is a single nanotube. This is reasonable because the tightest bundling of 3 smallest 1.2 nm nanotubes without any polymer would already result in a minimum bundle height of 2.2 nm (see figure S1(e)). The network on HOPG is shown in (a) and the corresponding cross-sections in (b), while (c) shows the network on silicon oxide and the resulting profiles in (d). In (b), profiles 1, 2, and 6 are close to or under 2 nm height, indicating that they are single or horizontally aligned nanotubes (no vertical bundling or stacking), while cross-sections 3, 4, 5 and 7 are close to or above 3 nm and therefore most likely bundles. The varying shape and height of the profiles indicate that there is a variety of bundles, the largest ones being close to 5 nm in height. Profiles in (d) show similar results with varying degrees of bundling, even though, at a first glance, the AFM image appears to show a network of uniform single nanotubes. S2
Fig. S1: Networks made of the same solution of polymer wrapped nanotubes, (a) on Piranha cleaned SiO 2, rinsed with toluene, (c) on Piranha cleaned SiO 2, rinsed with toluene, tetrahydrofuran and isopropanol sequentially, (e) on plasma cleaned SiO 2, rinsed with toluene, (g) on HOPG, rinsed with toluene. Cross-sections corresponding to numbered white lines in (a), (c), (e) and (d) are respectively shown in (b), (d), (f) and (h), indicating a significant amount of bundling. The cartoon in (i) shows that the height of a bundle of 3 1.2 nm diameter nanotubes is approximately 2.2 nm. S3
2. AFM tip size estimation and de-convolution procedure The de-convolving requires a good knowledge of the AFM probe s size. There are experimental methods to estimate the size by scanning a test sample prior to the imaging of the sample of interest, and use the sharpness of edges in images to deduce the shape of the AFM tip s end. While these methods may be adequate for average AFM probes, they are problematic for ultrasharp tips (tips whose radius is less than 10 nm approximately), because they the probes tend to degrade quickly and become more dull with each sample approach. Therefore, the tip size that is obtained on a test sample may no longer be true after scanning the test sample, removing the tip, and approaching the sample of interest and scanning it. Some analysis software, including Gwyddion 3, offer an automated blind tip estimation procedure that relies on an extensive analysis of the actual image of the sample of interest to infer the tip shape and size. While this seems like an ideal approach, upon testing it several times on nanotube networks images, we found that the resulting tip size was generally not in the realistic range. We are not sure why this is, but upon testing our impression was that this blind tip estimation algorithm worked better for AFM images of features that have aspect ratios closer to one, and less well for elongated features such as nanotubes. Another way to estimate the tip size relies on the fact that the Van der Waals force is directly proportional to the tip size. The equation describing the Van der Waals force between a spherical object (tip) and a flat substrate is: 6 (SE1) In SE1, F(d) is the Van der Waals force between the spherical AFM tip of radius r, and a plane (substrate) at a distance d, while A HAM is the Hamaker constant which depends on both the tip and the substrate materials. The AFM tip being a mechanical oscillator, the tip-sample force is also equal to: (SE2) In equation SE2, d is the AFM cantilever deflection, while k is it s spring constant, S D is the deflection sensitivity of the AFM and V VdW is the voltage signal corresponding to the maximum attractive force in the F(d) curve (while the AFM cantilever gets deflected when approaching the sample because of tip-sample interaction forces, this Fig. S2: AFM tip-sample force curve with the tip oscillating at 2 khz over the sample surface with the 300 nm amplitude. Blue curve shows the force as the tip approaches the surface, while the red curve shows it when the tip retracts away. Peak force tapping feedback is used. For tip size estimation we use the maximum of attractive force on the approach to avoid having to account for complicated chemical adhesion force that appears to dominate the retraction. S4
deflection is monitored using a photodiode, and therefore the signal that we detect is the voltage, which can then be converted into deflection by using the deflection sensitivity, a value that depends on several variables such as the laser alignment and the AFM instrument that is used; see figure S3 for a typical F(d) curve we saw in these experiments). The tip-sample Van der Waals force is still measurable a couple of nanometers away from the sample surface, while the repulsive tap forces are negligible even a fraction of nanometer away from the surface. There are other long range forces that can be relevant over the same tip-sample separation as the Van der Waals forces, the common ones being electrostatic interactions and snap-in capillary forces. However, both of these are readily detected as they modify the F(d) curve shape in characteristic ways. In our AFM experiments on nanotube networks we routinely monitor the F(d) curve and have never observed any evidence of either capillary or electrostatic tip-sample interactions. Therefore we can combine equations SE1 and SE2, which results in: (SE3) We have used the manufacturer-specified nominal spring constant k = 0.4 N/m, but for a more precise use of the method it would be advisable to determine this value experimentally for each of the tips. It is impossible to determine experimentally what is the value of d corresponding to the maximum of the attractive force, but generally values of 0.1 to 1 nm are considered to be reasonable. We have tested several of these values in the equation S3 on different AFM tips. In the end we have chosen to use d = 0.7 nm, because this value gives the radius of less than 3 nm and more than 2 nm for the smallest tips, and this is consistent with the manufacturer specified tip radius of 2 nm. In our experiments we used silicon nitride tips, and the substrate material is silicon oxide, and the Hamaker constant for these two materials is known 4. Finally, we have decided to use a value of S D = 60 nm/v for deflection sensitivity, instead of experimentally determining it for each of the experiments. This is a typical value we found in previous experiments for the same AFM probes with similar alignment on our AFM. This value can be determined at the time of each of the experiments, but doing it poses a risk of making ultra-sharp tip duller, increasing its radius, and the associated error as described here in part 2. We have recorded the value of V VdW before and after each of the images shown in the article, as shown in the table ST1, and have used these values and the equation SE3 to estimate corresponding tips sizes. Upon determining tip size we used the de-convolution procedure that s built in Gwyddion, namely the surface reconstruction function (Data Process Tip Surface Reconstruc on), where the input is the p size and the output the deconvolved image. It is important to note that Van der Waals force maxima on the substrate should be recorded before and after each image. Images where the before and after values are different should be discarded from the analysis because this change indicates that the tip has undergone a change at some point during the scanning (either a piece of the tip was lost, resulting in a duller tip with a larger diameter, or the tip got contaminated picking some contaminant from the surface), and therefore the volumetric analysis would become unreliable. S5
3. Deconvoluted images Fig. S3 Deconvoluted 1 μm 2 AFM images of nanotube networks on SiO 2 (a, b, c) and on HOPG (d). Substrates were cleaned by Piranha etching (a, b), oxygen plasma treatment (c), or by cleaving (d) before the network deposition. Upon solvent evaporation networks were rinsed with toluene for 20 seconds (a,c,d) or sequentially with toluene, isopropanol and tetrahydrofuran, for 20 seconds each (b). Table ST1: The top line of the table shows the raw voltage values of the Van der Waals force maxima (V VdW ) that were recorded before and after each of the scans shown in figure S3, while the bottom line shows the radii values that was calculated using these voltages using the equation SE3 S6
4. Uncertainty based on the choice of the height threshold to separate nanotubes from the substrate In this article we propose a novel analysis method, and the uncertainty that we discuss here is only related to the analysis, and not to the experimental technique (AFM) or the sample preparation uncertainties. There are two Fig. S1: An estimate of the maximum accuracy range that can result from the choice of height threshold that defines the network (in blue) as everything above the threshold, and the substrate as everything that is lower. For the network that was deposited on piranha cleaned silicon oxide, and rinsed with toluene post-deposition, our best estimate of the threshold was 1.7 nm, as shown in the top row middle column above. Then, we estimated that varying the threshold by 0.25 nm lower or higher corresponded to a maximum error range, out of which most individual users would realize that either large portions of the substrate (top left side image), or, respectively, of the network (top right side image) are being identified as network, or, respectively, as substrate. Upon setting the threshold we manually removed any part of the mask that was obviously on the substrate using appropriate tools in Gwyddion, resulting in images in the second row. These cleaned images in the second row were then analyzed using the procedure outlined in the article to estimate the network density and the bundling coefficient, and these numbers were used to determine the final uncertainty of the analysis for this image, i.e. ± 8 μm -2 for the network density, and ± 0.03 for the bundling coefficient. S7
main sources of uncertainty that affect the analysis method: - The bias towards underestimating the number of nanotubes, which we have demonstrated in part 2 above. Based on the analysis in part 2, this uncertainty does not affect single nanotubes, but appears to significantly affect larger bundles. To eliminate this bias we have added the de-convolution procedure to the analysis method, but the de-convolution introduces a whole new set of uncertainties, related both to the tip size determination, and to the de-convolution algorithm. In conclusion, this part of the analysis is too complex to precisely determine the associated uncertainty of each separate variable. One way to go around this would be to perform tests on well characterized samples simulating different bundle sizes and experimentally determine the uncertainty using the top-down approach. At this time we have not yet done this. However, this uncertainty is not affected by the person who carries out the analysis, and always introduces the same bias for the same sample, and therefore, even if it is not accounted for, it affects only the absolute values, but does not affect relative comparisons between sample preparations. - The uncertainty due to the choice of the height threshold that defines what part of the image is the network (shown in blue in figure S4) and what part is the substrate. This uncertainty depends on the personal appreciation of the image, and may vary both depending on the person, and on the day to day variability even for the same individual performing the analysis. We have tested what happens when one person performs the analysis several times and on the same set of images, but sometimes with more than a month in-between, and the spread of results was generally smaller than the uncertainty that we estimated using the method described below. We established the uncertainty range resulting from the threshold choice by first finding the best estimate of the threshold, and then seeing what happens if we change this threshold value to a point where the errors become obvious. In the case of the network deposited on piranha cleaned silicon oxide and rinsed with toluene following the deposition, our best estimate of the threshold was 1.7 nm, as shown in the top row middle column in figure S4. Then, we estimated that varying the threshold by 0.25 nm lower, or higher, corresponded to a maximum error range, where most individual users would realize that either large portions of the substrate (top left side image in S4), or, respectively, of the network (top right side image) are being identified as the network, or, respectively, as the substrate. Upon setting the threshold, we manually removed any part of the mask that was obviously on the substrate using appropriate tools in Gwyddion (filtering grains by pixel-size, or using the remove individual grains tool), resulting in images in the second row of S4. These cleaned images in the second row were then analyzed using the procedure outlined in the article to estimate the network density and the bundling coefficient, as shown in the table in the bottom of S4, and these numbers were used to determine the final uncertainty of the analysis for this image, i.e. ± 8 μm -2 for network density, and ± 0.03 for the bundling coefficient. The same procedure, that is varying the best threshold by + and 0.25 nm was found to be adequate for all the networks. 5. References 1 J. Ding, Z. Li, J. Lefebvre, F. Cheng, G. Dubey, S. Zou, P. Finnie, A. Hrdina, L. Scoles, G. P. Lopinski, C. T. Kingston, B. Simard and P. R. L. Malenfant, Nanoscale, 2014, 6, 2328 2 P. Klapetek, M. Valtr, D. Nečas, O. Salyk and P. Dzik, Nanoscale Res. Lett., 2011, 6, 514. 3 D. Nečas and P. Klapetek, Cent. Eur. J. Phys., 2012, 10, 181. 4 L. Bergstrom, Adv. Colloid Interface Sci., 1997, 70, 125. S8